Physicists Watch Atoms Spinning in Opposite Directions Inside a Crystal for the First Time, Decoding a Strange '1 + 1 = -1' Rule of Lattice Motion

An international team of physicists has, for the first time, directly observed angular momentum being passed between vibrating atoms inside a crystal — and, in doing so, has caught a long-predicted bit of quantum bookkeeping in the act of breaking ordinary intuition. When two clockwise rotations combined inside the crystal, the resulting motion did not spin twice as fast in the same direction. It spun at twice the frequency in the opposite direction. The researchers call the rule "1 + 1 = -1," and it is the experimental signature of an Umklapp process, a Bavarian word meaning roughly "folding over" that the German physicist Rudolf Peierls coined in 1929 to describe an exception to the everyday law of momentum conservation.

The study, published Tuesday in Nature Physics under the title "Direct observation of angular momentum transfer among crystal lattice modes," was led by Sebastian Mährlein of the Helmholtz-Zentrum Dresden-Rossendorf (HZDR) and Tobias Kampfrath at the Fritz Haber Institute of the Max Planck Society in Berlin, with collaborators at Forschungszentrum Jülich, the Max Born Institute and Spain's Donostia International Physics Center. The team used pairs of intense, perpendicularly polarized terahertz laser pulses — pulses with electric fields strong enough to push atoms several picometers off their equilibrium positions — to drive coherent circular vibrations in bismuth selenide, a layered quantum material best known as a topological insulator.

By varying the time delay between the two pulses with attosecond precision and by reading out the resulting motion through a separate near-infrared probe pulse, the researchers mapped how the angular momentum of one circular vibrational mode (a "chiral phonon") flowed into a second mode at a higher frequency. The Umklapp rule, predicted by theorists for decades but never previously demonstrated, kicked in when the combined wavevector exceeded the edge of the crystal's Brillouin zone — at which point the lattice's six-fold rotational symmetry forced the resulting motion to fold backward through reciprocal space, reversing its handedness.

"This is the kind of measurement people have wanted to do for half a century," said Mährlein in a statement released by HZDR. "Phonon angular momentum was always treated as a bookkeeping device — useful for theory, but hard to see. We can now watch it move, and we can steer where it goes." The team's setup gives experimenters a new knob for controlling magnetism and spin transport in quantum materials, since chiral phonons couple directly to electron spins through a mechanism known as the phonon spin Hall effect. Several recent papers have suggested chiral phonons could be the missing ingredient explaining ultrafast demagnetization in metals.

Outside experts said the work is likely to spur a wave of follow-up experiments. "Direct observation of a phonon Umklapp event is genuinely a first, and the choice of bismuth selenide is clever because the topology of the bands amplifies the signal," said Lucile Savary, a condensed-matter theorist at the École Normale Supérieure in Lyon who was not involved in the study. The HZDR team is already planning experiments on the related material bismuth telluride and on the recently discovered altermagnets — a new class of magnetic material identified at Charles University in Prague last year — to test whether the same Umklapp rule governs angular momentum exchange in materials with very different symmetries.